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This paper presents the schedulability analysis for control messages when networked control loops, built on top of the controller area network (CAN), are dynamically allocating bandwidth in terms of their controlled plants' dynamics. The bandwidth allocation policy is theoretically described by an optimization problem and practically solved by the distributed bitwise arbitration of CAN messages when message identifiers, i.e., priorities, reflect control applications demands. This poses the problem of assessing whether the set of real-time messages will meet their deadlines regardless of run-time priority changes. This is solved by a schedulability analysis based on recent results on worst-case response time techniques for real-time CAN applications. The analysis ends up with the schedulability test for this type of applications.